Covariant Open String Field Theory Research Articles

Covariant open string field theory on multiple Dp-branes**Supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (2017R1D1A1A02017805)

We study covariant open bosonic string field theories on multiple Dp-branes by using the deformed cubic string field theory, which is equivalent to string field theory in the proper-time gauge. Constructing the Fock space representations of the three-string vertex and the four-string vertex on multiple Dp-branes, we obtain the field theoretical effective action in the zero-slope limit. On multiple D0-branes, the effective action reduces to the Banks-Fishler-Shenker-Susskind (BFSS) matrix model. We also discuss the relation between open string field theory on multiple D-instantons in the zero-slope limit and the Ishibashi-Kawai-Kitazawa-Tsuchiya (IKKT) matrix model. The covariant open string field theory on multiple Dp-branes could be useful to study the non-perturbative properties of quantum field theories in (p + 1)-dimensions in the framework of the string theory. The non-zero-slope corrections may be evaluated systematically by using covariant string field theory.

Entanglement entropy for open bosonic strings on Dp-branes

We study the entanglement entropy for open bosonic strings on multiple Dp-branes by using the covariant open string field theory. Choosing one of the spatial coordinates which are tangential to the hyperplane on which Dp-branes are located, we divide the hyperplane into two halves. By using the string wavefunction in the Fock space representation, we evaluate the entanglement entropy. The entanglement entropy is found to be proportional to the area of (p−1)-dimensional boundary of the bipartite hyperplanes and divergent in the ultraviolet (UV) region as well as in the infrared (IR) region. However, the leading divergences are mainly due to tachyon contributions to the entanglement entropy, which may be absent in supersymmetric string theories. Apart from the divergences thanks to tachyons, the entanglement entropy for open bosonic strings on Dp-branes is finite for 2≤p≤dcritical−2 and logarithmically divergent for p=1,dcritical−1.

Gravitational Scattering Amplitudes and Closed String Field Theory in the Proper-Time Gauge

We construct a covariant closed string field theory by extending recent works on the covariant open string field theory in the proper-time gauge. Rewriting the string scattering amplitudes generated by the closed string field theory in terms of the Polyakov string path integrals, we identify the Fock space representations of the closed string vertices. We show that the Fock space representations of the closed string field theory may be completely factorized into those of the open string field theory. It implies that the well known Kawai-Lewellen-Tye (KLT) relations of the first quantized string theory may be promoted to the second quantized closed string theory. We explicitly calculate the scattering amplitudes of three gravitons by using the closed string field theory in the proper-time gauge.

Manifestly covariant, gauge-invariant interacting closed-string field theory

We argue that Witten's covariant open-string field theory already implies its covariant closed-string field theory analog. The respective analog closedstring field theory is explicitly exhibited.

Covariant closed string theory cannot be cubic

We show that no symmetric three-closed-string vertex can give dual off-shell amplitudes for four-string scattering. This implies that covariant closed string field theory cannot be cubic. We conjecture the necessity of non-polynomiality. Our result implies the uniqueness of the cubic formulation of covariant open string field theory.

DERIVING THE FOUR-STRING AND OPEN-CLOSED STRING INTERACTIONS FROM GEOMETRIC STRING FIELD THEORY

One of the baffling questions concerning the covariant open string field theory is why there are two distinct BRST theories and why the four-string interaction appears in one version but not the other. We solve this mystery by showing that both theories are gauge-fixed versions of a higher gauge theory, called the geometric string field theory, with a new field, a string vierbein [Formula: see text], which allows us to gauge the string length and σ-parametrization. By fixing the gauge, we can derive the “endpoint gauge” (the covariantized light cone gauge), the “midpoint gauge” of Witten, or the “interpolating gauge” with arbitrary string lengths. We show explicitly that the four-string interaction is a gauge artifact of the geometric theory (the counterpart of the four-fermion instantaneous Coulomb term of QED). By choosing the interpolating gauge, we produce a new class of four-string interactions which smoothly interpolate between the endpoint gauge and the midpoint gauge (where it vanishes). Similarly, we can extract the closed string as a bound state of the open string, which appears in the endpoint gauge but vanishes in the midpoint gauge. Thus, the four-string and open-closed string interactions do not have to be added to the action as long as the string vierbein is included.

A Gauge Invariant Action Containing Both Open and Closed String Fields

An interesting feature of the covariant open string field theory is that the closed string appears as a bound state of the open string.),2) This suggests the existence in open string field theory of a larger gauge symmetry which includes general coordinate transformation. Motivated by this, Hata and N ojiri proposed a new transformation on the open string field) with closed string functional parameter in the formulation of string field theory proposed in Refs. 4) and 5). The structure of the transformation and its algebra are those of stringy general coordinate transformation known in the closed string field theory.5) The gauge invariant open string action is, however, invariant under only the global part of the transformation.. It seems to contradict the existence of the closed string pole in open string one-loop amplitude which is computed from the BRS invariant action. On the basis of a covariant string field theory constructed by Kyoto group,4),5) we propose a new covariant action which contains both open and closed string fields and· is invariant not only under the gauge transformation in the usual open string theory but also under stringy general coordinate transformation. Since the action contains only the interaction terms as in case of the pre-geometrical cubic action in Ref. 6) or Ref. 7), it is background independent. The kinetic term is generated through field condensation of the fields. We investigate the form of the action after the field condensation correspondIng to the flat background. The relation between the new action and the BRS invariant action of Ref. 4) is also discussed in this paper. Before constructing the new action, we define several operations on string fields. First we' define the transition from an open ·string field (j) to a closed string field (denoted by «(j)) and that from a closed string field A to an open string field [A] as follows:*) .

New symmetry in covariant open-string field theory.

We construct a new symmetry transformation in a covariant formulation of open-string field theory. It has a closed-string functional as its transformation parameter and consists of open-closed and open-open-closed string vertices. The structure of the transformation and its algebra are those of the (stringy) general coordinate transformation known in the closed-string field theory. However, because of the constraint on the transformation parameter necessary for the action invariance, the present transformation is restricted to represent only the global part of it.

On the quantization of string field theory

The quantization of free, gauge-fixed and covariant open-string field theory is examined. It is noted that the BRST symmetry of the world sheet is not exactly relevant for second quantization. An extra local symmetry in the auxiliary sector requires a gauge-fixing condition, which then breaks the BRST symmetry. The remaining BRST symmetries are identified and are shown to contain the “physical” BRST symmetry, which corresponds to the BRST symmetry found in the usual Yang-Mills theories. The gauge-fixing and ghost lagrangian is written as an anticommutator of the sum of the surviving BRST charges and a bilinear in field operators.